Salomon, Shalit and Shamovich proved in [1]} that \(\mathcal {H}^2_d\)  has the following non-commutative version of the Pick property: let \(\Omega \)  be a subset of \(\mathcal {B}_d\) , and let \(\overline{\Omega }^{nc}\)  be its NC-envelop, that is, the smallest NC set containing \(\Omega \)  that is also closed under left intertwiners:
\(W\in \overline{\Omega }^{nc}\Rightarrow P^{-1}WP\in \overline{\Omega }^{nc}.\) 
